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This article is the second within a three-part series on Fourier ptychography, which is a computational microscopy technique for high-resolution, large field-of-view imaging. While the first article laid out the basics of Fourier ptychography, this second part sheds light on its algorithmic ingredients. We present a non-technical discussion of phase retrieval, which allows for the synthesis of high-resolution images from a sequence of low-resolution raw data. Fourier ptychographic phase retrieval can be carried out on standard, widefield microscopy platforms with the simple addition of a low-cost LED array, thus offering a convenient alternative to other phase-sensitive techniques that require more elaborate hardware such as differential interference contrast and digital holography.

Fourier ptychography is an emerging computational microscopy technique that can generate gigapixel-scale images of biological samples. With only the addition of a low-cost LED array to a standard digital microscope and a reconstruction algorithm, Fourier ptychography overcomes the fundamental trade-off between a microscope's resolution and field-of-view without any moving parts. This article is the first in a three-part series that aims to introduce the fundamentals of the technology to the broader microscopy community and beyond, using intuitive explanations.